The following is a collection of random facts observations I made while reading Lehmann & Romano "Testing Statistical Hypotheses" (3rd ed.) and Lehmann & Casella "Theory of Point Estimation" (2nd ed.), abbr. TSH and TPE. The choice of topics is biased towards application in regression models.

• On the notion of unbiasedness of estimators, hypotheses tests, and confidence intervals

• Conditional expectation, conditional distribution, sufficiency, decision procedures

• An informal summary of Neyman-Pearson and generalizations

• Permutation tests

• UMP tests for two-sided hypotheses

• Least squares estimators are nice! PART 1 (UMVU, MRE, BLUE)

• Least squares estimators are nice! PART 2 (consistency, asymptotic normality and efficiency)

• UMP invariant tests for linear models

• Robustness of hypotheses tests in linear models

• Asymptotic tests and confidence regions for linear mixed models

• Bootstrap confidence intervals and hypotheses tests for linear mixed models